Free vibration of cantilevered cylinders: Effects of cross-sections and cavities
type: Item
instance of: scholarly article
title: Free vibration of cantilevered cylinders: Effects of cross-sections and cavities
zbMATH Open document ID: 0869.73040
DOI: 10.1007/BF01212632
author: Yanyan Li
published in: Acta Mechanica
publication date: 1997-08-20T00:00:00Z
review text: The influence of a cavity on natural frequencies and mode shapes of a homogeneous, isotropic, elastic solid cylinder is studied. A numerical algorithm is proposed to examine the vibrations of elastic cylinders with a deep cavity. The technique uses three-dimensional elasticity theory in conjunction with the Ritz form of minimum energy to derive the governing eigenvalue equation. Within the context of three-dimensional elasticity, displacement functions composed of a set of two-dimensional lateral surface functions and one-dimensional longitudinal functions are defined for each displacement component. The technique yields upper-bound on natural frequencies and three-dimensional deformed mode shapes for a range of elastic hollow cylinders.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74S30
zbMATH DE Number: 940969
zbMATH Keywords: mode shapes
zbMATH Keywords: three-dimensional elasticity theory
zbMATH Keywords: Ritz form of minimum energy
zbMATH Keywords: eigenvalue equation
zbMATH Keywords: upper-bound natural frequencies
reviewed by: J. Genin
MaRDI profile type: Publication
cites work: The Shear Coefficient in Timoshenko’s Beam Theory
cites work: Vibrations of Solid Cylinders
cites work: Vibrations of Free Hollow Circular Cylinders
cites work: Vibration of Stress-Free Hollow Cylinders of Arbitrary Cross Section
cites work: Three-dimensional elasticity solutions to vibration of cantilevered skewed trapezoids
cites work: Free Vibration Studies on Stress-Free Three-Dimensional Elastic Solids
cites work: On the three-dimensional vibrations of the cantilevered rectangular parallelepiped
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description: scientific article; zbMATH DE number 940969